On Connectedness via a G-method and a Hereditary Class

Abstract

In 2003, Connor and Grosse-Erdmann [1] introduced the definition of $G$-method by using G-linear functions instead of limit, based on various types of convergence on real numbers. Later on, some mathematicians examined this concept in topological groups. Then new concepts, which were important in topology such as $G$-sequential compactness and $G$-sequential connected, were defined and some properties of those concepts are investigated. S. Lin and L. Liu defined $G$-method notion by taking any set instead of topological group in 2016. In this paper, we give definition of $cl_{G^{*}}$-closure which is more general than $G$-closure of a set with the help of hereditarily class. Then we define the notion of $\tau_{G^{*}}$-topology and give the concepts of $G^{*}$-connected and $G^{*}$-component. Besides, we examine the relationship between these concepts and previously given concepts.

Keywords

• hereditary class
• G-method
• G*-closed
• G*-connected
• G*-component

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